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            <h1 style="display: none">二进制中1的个数</h1>
            
              <p class="note note-info">
                
                  本文最后更新于：2022年1月2日 下午
                
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            <div class="markdown-body">
              <h3 id="tips">Tips</h3>
<blockquote>
<p>《编程之美》 记录</p>
</blockquote>
<h4 id="解法一-除法">解法一 ： 除法</h4>
<figure class="highlight dart"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><code class="hljs dart"><span class="hljs-built_in">int</span> count(<span class="hljs-built_in">int</span> v)&#123;<br>    <span class="hljs-built_in">int</span> <span class="hljs-built_in">num</span> = <span class="hljs-number">0</span>;<br>    <span class="hljs-keyword">while</span>(v)&#123;<br>        <span class="hljs-keyword">if</span>(v % <span class="hljs-number">2</span> == <span class="hljs-number">1</span>)<br>            <span class="hljs-built_in">num</span>++;<br>        v /= <span class="hljs-number">2</span>;<br>    &#125;<br>    <span class="hljs-keyword">return</span> <span class="hljs-built_in">num</span><br>&#125;<br></code></pre></td></tr></table></figure>
<h4 id="解法二-位运算">解法二 ： 位运算</h4>
<blockquote>
<p>效率较解法 一 较高 ， 时间复杂度 O（log<sub>2</sub>n ）</p>
</blockquote>
<figure class="highlight dart"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><code class="hljs dart"><span class="hljs-built_in">int</span> count(<span class="hljs-built_in">int</span> v)&#123;<br>    <span class="hljs-built_in">int</span> <span class="hljs-built_in">num</span> = <span class="hljs-number">0</span>;<br>    <span class="hljs-keyword">while</span>(v)&#123;<br>        <span class="hljs-keyword">if</span>(v &amp; <span class="hljs-number">1</span>)<br>            <span class="hljs-built_in">num</span>++;<br>        v &gt;&gt;= <span class="hljs-number">1</span>;<br>    &#125;<br>    <span class="hljs-keyword">return</span> <span class="hljs-built_in">num</span>;<br>&#125;<br></code></pre></td></tr></table></figure>
<h4 id="解法三">解法三</h4>
<blockquote>
<p>让算法复杂度只与 二进制数中 1 的个数有关， 当然最坏情况下 为
O(log<sub>2</sub>n)</p>
</blockquote>
<figure class="highlight dart"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><code class="hljs dart"><span class="hljs-built_in">int</span> count(<span class="hljs-built_in">int</span> v)&#123;<br>    <span class="hljs-built_in">int</span> <span class="hljs-built_in">num</span> = <span class="hljs-number">0</span>;<br>    <span class="hljs-keyword">while</span>(v)&#123;<br>        v = v &amp; (v - <span class="hljs-number">1</span>);  <span class="hljs-comment">// 依次将最右面的 1 消去</span><br>        <span class="hljs-built_in">num</span>++;<br>    &#125;<br>    <span class="hljs-keyword">return</span> <span class="hljs-built_in">num</span>;<br>&#125;<br></code></pre></td></tr></table></figure>
<h4 id="解法四-分支运算">解法四 : 分支运算</h4>
<blockquote>
<p>把所有结果都罗列出来， 不可取</p>
</blockquote>
<h4 id="解法五-查表">解法五 ： 查表</h4>
<blockquote>
<p>空间换时间， 复杂度O(1), 需谨慎使用, 以下为 0 到 255 的</p>
</blockquote>
<figure class="highlight autohotkey"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br></pre></td><td class="code"><pre><code class="hljs autohotkey">int countTable[<span class="hljs-number">256</span>] = &#123;<br><span class="hljs-built_in">    1,</span> <span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>,<br><span class="hljs-built_in">    1,</span> <span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    1,</span> <span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    3,</span> <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>,<br><span class="hljs-built_in">    1,</span> <span class="hljs-number">2</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    3,</span> <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>,<br><span class="hljs-built_in">    2,</span> <span class="hljs-number">3</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>,<br><span class="hljs-built_in">    3,</span> <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>,<br><span class="hljs-built_in">    3,</span> <span class="hljs-number">4</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>,<br><span class="hljs-built_in">    4,</span> <span class="hljs-number">5</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span><br>&#125;<span class="hljs-comment">;</span><br><br>int Count(int v)&#123;<br>    <span class="hljs-keyword">return</span> countTable(v)<span class="hljs-comment">;</span><br>&#125;<br></code></pre></td></tr></table></figure>

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